General description
This module covers a number of mathematical topics that are relevant to students studying Economics. These include functions, the concepts and rules of differentiation, optimisation of functions of one variable and integration. The application of this material to problems in Economics forms an important element of this module.

Aims
To introduce students to some of the elementary but essential mathematical concepts and skills necessary for an understanding of modern economic theories.

Learning outcomes
On completion of this module, a student should be able to:

• evaluate powers of a number where the exponent is positive, negative, whole or fractional;
• simplify algebraic expressions using the rules of exponents;
• solve linear and quadratic equations;
• determine the equilibrium price and quantity for single-commodity and multi-commodity markets;
• use the function notation, y = f(x);
• determine the inverse of a function;
• sketch the graphs of linear and quadratic functions;
• find the slope of a straight line given any two points on the line;
• use both notations, f'(x) and dy/dx, for the derivative of a function;
• differentiate simple polynomial functions and functions of the form f(x) + g(x), f(x)-g(x);
• evaluate second-order derivatives;
• calculate marginal revenue and marginal cost;
• calculate marginal product of labour;
• calculate marginal propensity to consume and marginal propensity to save;
• describe the use of the exponential function in economic modelling;
• sketch graphs involving the exponential function;
• differentiate the exponential and natural logarithm functions;
• evaluate logarithms in simple cases;
• use the laws of logarithms to solve equations;
• explain how to investigate the returns to scale of a production function;
• calculate the future value of a principal under monthly, annual and continuous compounding;
• determine the annual percentage rate of interest given a nominal rate of interest;
• find and classify the stationary points of a function;
• find the maximum and minimum points of an economic function.

Syllabus
1. ELEMENTARY ALGEBRA: Exponents. Polynomials. Factorization. Solution of linear and quadratic equations. Solution of simultaneous equations. Supply and demand analysis.
2. FUNCTIONS: Notation and definitions. Graphs of functions. Inverse functions. Budget lines. Economic functions.
3. DIFFERENTIATION: The derivative of a function. The derivative of a polynomial. Marginal functions. Higher-order derivatives.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS: Definitions and properties. Graphs of exponential and logarithmic functions. Derivatives. Solution of logarithmic equations. Production functions. Interest compounding.
5. OPTIMIZATION OF FUNCTIONS OF A SINGLE VARIABLE: Local and global maxima and minima, points of inflection. Optimization of economic functions.